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simplify into a single fraction and write your answer in terms of sin x and cos x: tan x + 1/tan x
 one year ago
 one year ago
P>Q Group Title
simplify into a single fraction and write your answer in terms of sin x and cos x: tan x + 1/tan x
 one year ago
 one year ago

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ZeHanz Group TitleBest ResponseYou've already chosen the best response.0
Hint: tanx=sinx/cosx, so 1/tanx=cosx/sinx. You now only need to write the sum of these as one fraction!
 one year ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
so sin^2x + Cos^2x/cosxsinx ?
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
yes  that is correct but you can simplify this further.\[\sin^2(x)+\cos^2(x)=?\]
 one year ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
o um (sinx)(sinx) + (cosx)(cosx)/cosxsinx
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
no, the equation I wrote up there is a well know trig identity  look it up in your notes, you must have been taught this at some stage.
 one year ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
Pythagorean trig identity
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
so now make use of that fact to simplify your expression
 one year ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
ya idk, I just kinda put it out sin^2x + Cos^2x/cosxsinx = 1 im not seeing how this relates it just made it worse,.
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
the identity you need to use is:\[\sin^2(x)+\cos^2(x)=1\]
 one year ago

P>Q Group TitleBest ResponseYou've already chosen the best response.0
what do u mean, this has nothing to do with this problem lol I mean all I know is that is the Pythagorean tri identity and that you can move cos or sin and lets say u move sin it goes to the right and u have cos^2(x) = plus or minus radical 1sin^2(x)
 one year ago

asnaseer Group TitleBest ResponseYou've already chosen the best response.0
Look at the steps you took in this problem:\[\begin{align} \tan(x)+\frac{1}{\tan(x)}&=\frac{\sin(x)}{\cos(x)}+\frac{\cos(x)}{\sin(x)}\\ &=\frac{\sin^2(x)+\cos^2(x)}{\cos(x)\sin(x)} \end{align}\]now notice that the numerator contains the terms: \(\sin^2(x)+\cos^2(x)\), and you know that this identity always equals 1. Therefore you can replace \(\sin^2(x)+\cos^2(x)\) by 1.
 one year ago
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